Journal of Function Spaces The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Strong Summability of Fourier Transforms at Lebesgue Points and Wiener Amalgam Spaces Wed, 02 Sep 2015 12:54:07 +0000 We characterize the set of functions for which strong summability holds at each Lebesgue point. More exactly, if is in the Wiener amalgam space and is almost everywhere locally bounded, or , then strong -summability holds at each Lebesgue point of . The analogous results are given for Fourier series, too. Ferenc Weisz Copyright © 2015 Ferenc Weisz. All rights reserved. Shifting and Variational Properties for Fourier-Feynman Transform and Convolution Tue, 01 Sep 2015 11:32:03 +0000 Shifting, scaling, modulation, and variational properties for Fourier-Feynman transform of functionals in a Banach algebra are given. Cameron and Storvick's translation theorem can be obtained as a corollary of our result. We also study shifting, scaling, and modulation properties for the convolution product of functionals in . Byoung Soo Kim Copyright © 2015 Byoung Soo Kim. All rights reserved. Weighted Weak Local Hardy Spaces Associated with Schrödinger Operators Tue, 01 Sep 2015 06:28:38 +0000 We characterize the weighted weak local Hardy spaces related to the critical radius function and weights which locally behave as Muckenhoupt’s weights and actually include them, by the atomic decomposition. As an application, we show that localized Riesz transforms are bounded on the weighted weak local Hardy spaces. Hua Zhu Copyright © 2015 Hua Zhu. All rights reserved. Choi-Davis-Jensen Inequalities in Semifinite von Neumann Algebras Mon, 31 Aug 2015 11:41:25 +0000 We prove the Choi-Davis-Jensen type submajorization inequalities on semifinite von Neumann algebras for concave functions and convex functions. Turdebek N. Bekjan, Kordan N. Ospanov, and Asilbek Zulkhazhav Copyright © 2015 Turdebek N. Bekjan et al. All rights reserved. On Approximate Controllability of Second-Order Neutral Partial Stochastic Functional Integrodifferential Inclusions with Infinite Delay and Impulsive Effects Sun, 30 Aug 2015 08:23:40 +0000 We discuss the approximate controllability of second-order impulsive neutral partial stochastic functional integrodifferential inclusions with infinite delay under the assumptions that the corresponding linear system is approximately controllable. Using the fixed point strategy, stochastic analysis, and properties of the cosine family of bounded linear operators combined with approximation techniques, a new set of sufficient conditions for approximate controllability of the second-order impulsive partial stochastic integrodifferential systems are formulated and proved. The results in this paper are generalization and continuation of the recent results on this issue. An example is provided to show the application of our result. Zuomao Yan Copyright © 2015 Zuomao Yan. All rights reserved. Functions of Bounded th -Variation and Continuity Modulus Sun, 23 Aug 2015 09:32:14 +0000 A scale of spaces exists connecting the class of functions of bounded th -variation in the sense of Riesz-Merentes with the Sobolev space of functions with -integrable th derivative. This scale is generated by the generalized functionals of Merentes type. We prove some limiting relations for these functionals as well as sharp estimates in terms of the fractional modulus of smoothness of order . Odalis Mejía and Pilar Silvestre Copyright © 2015 Odalis Mejía and Pilar Silvestre. All rights reserved. Positive Solutions of Two-Point Boundary Value Problems for Monge-Ampère Equations Thu, 20 Aug 2015 08:52:48 +0000 This paper considers the following boundary value problem: , where is odd. We establish the method of lower and upper solutions for some boundary value problems which generalizes the above equations and using this method we present a necessary and sufficient condition for the existence of positive solutions to the above boundary value problem and some sufficient conditions for the existence of positive solutions. Baoqiang Yan and Meng Zhang Copyright © 2015 Baoqiang Yan and Meng Zhang. All rights reserved. New Fixed Point Results for Fractal Generation in Jungck Noor Orbit with -Convexity Wed, 12 Aug 2015 07:56:46 +0000 We establish new fixed point results in the generation of fractals (Julia sets, Mandelbrot sets, and Tricorns and Multicorns for linear or nonlinear dynamics) by using Jungck Noor iteration with -convexity. Shin Min Kang, Waqas Nazeer, Muhmmad Tanveer, and Abdul Aziz Shahid Copyright © 2015 Shin Min Kang et al. All rights reserved. A Generalization for Theorems of Datko and Barbashin Type Tue, 11 Aug 2015 12:58:08 +0000 The goal of the paper is to give some characterizations for the uniform exponential stability of evolution families by unifying the discrete-time versions of the Barbashin-type theorem and the Datko-type theorem. Pham Viet Hai Copyright © 2015 Pham Viet Hai. All rights reserved. A Probabilistic Fixed Point Result Using Altering Distance Functions Mon, 10 Aug 2015 13:24:17 +0000 We prove a general fixed point theorem in Menger spaces for mappings satisfying a contractive condition of Ćirić type, formulated by means of altering distance functions. Thus, we extend some recent results of Choudhury and Das, Miheţ, and Babačev and also clarify some aspects regarding a theorem of Choudhury, Das, and Dutta. Claudia Zaharia and Nataša Ćirović Copyright © 2015 Claudia Zaharia and Nataša Ćirović. All rights reserved. Approximate Controllability of the Degenerate System with the First-Order Term Wed, 05 Aug 2015 06:47:32 +0000 We consider the approximate controllability of the degenerate system with the first-order term. The first-order term in the equation cannot be controlled by the diffusion term. The system is shown to be approximately controllable by constructing a control by means of its conjugate problem. Runmei Du Copyright © 2015 Runmei Du. All rights reserved. Rough Multilinear Fractional Integrals on Weighted Morrey Spaces Mon, 03 Aug 2015 09:08:04 +0000 It is showed that a class of multilinear fractional operators with rough kernels, which are similar to the higher-order commutators for the rough fractional integrals, are bounded on the weighted Morrey spaces. Xiao Li and Runqing Cui Copyright © 2015 Xiao Li and Runqing Cui. All rights reserved. Gain of Regularity in Extension Problem on Convex Domains Tue, 21 Jul 2015 08:18:10 +0000 We investigate the extension problem from higher codimensional linear subvarieties on convex domains of finite type. We prove that there exists a constant such that on Bergman spaces with there appears the so-called “gain regularity.” The constant depends on the minimum of the dimension and the codimension of the subvariety. This means that the space of functions which admit an extension to a function in the Bergman space is strictly larger than , where is a subvariety. M. Jasiczak Copyright © 2015 M. Jasiczak. All rights reserved. The Spaces of Functions of Two Variables of Bounded -Variation in the Sense of Schramm-Korenblum Tue, 07 Jul 2015 06:53:59 +0000 The purpose of this paper is twofold. Firstly, we introduce the concept of bounded -variation in the sense of Schramm-Korenblum for real functions with domain in a rectangle of . Secondly, we study some properties of these functions and we prove that the space generated by these functions has a structure of Banach algebra. A. Azócar, O. Mejía, N. Merentes, and S. Rivas Copyright © 2015 A. Azócar et al. All rights reserved. On Mann’s Type Method for Nonexpansive and Strongly Quasinonexpansive Mappings in Hilbert Spaces Thu, 02 Jul 2015 11:58:57 +0000 In the setting of Hilbert spaces, we study Mann’s type method to approximate strong solutions of variational inequalities. We show that these solutions are fixed points of a nonexpansive mapping and/or a strongly quasinonexpansive mapping, depending on the coefficients involved in the algorithm. Nawab Hussain, Giuseppe Marino, and Badriah A. S. Alamri Copyright © 2015 Nawab Hussain et al. All rights reserved. Multiplicative Isometries on Classes of Holomorphic Functions Mon, 29 Jun 2015 08:32:25 +0000 In (Iida and Kasuga 2013), the authors described multiplicative (but not necessarily linear) isometries of onto in the case of positive integer , where    is included in the Smirnov class . In this paper, we will generalize the result to arbitrary (not necessarily positive integer) value of the exponents . Yasuo Iida and Kazuhiro Kasuga Copyright © 2015 Yasuo Iida and Kazuhiro Kasuga. All rights reserved. A Simple Repairable System with Warning Device Thu, 25 Jun 2015 11:14:21 +0000 This paper considers a simple repairable system with a warning device which can signal an alarm when the system is not in good condition and a repairman who can have delayed-multiple vacations. By using Markov renewal process theory and the probability analysis method, the system is first described into a group of integrodifferential equations. Then the unique existence and asymptotic stability, especially the exponential stability of the system dynamic solution, are studied by using the strongly continuous semigroup theory or semigroup theory and the spectrum theory. The reliability indices and some applications (such as the comparisons of some indexes and profit of systems with and without warning device) as well as numerical examples are presented at the end of the paper. Xiao Zhang and Lina Guo Copyright © 2015 Xiao Zhang and Lina Guo. All rights reserved. Commutators of Multilinear Singular Integrals on Weighted Herz Spaces Tue, 23 Jun 2015 10:38:04 +0000 Suppose , is the iterated commutator of and the -linear Calderón-Zygmund operator . The purpose of this paper is to discuss the boundedness properties of on weighted Herz spaces with general Muckenhoupt weights. Baozhen Wang and Huimin Wang Copyright © 2015 Baozhen Wang and Huimin Wang. All rights reserved. Generalized Projections on Closed Nonconvex Sets in Uniformly Convex and Uniformly Smooth Banach Spaces Tue, 23 Jun 2015 06:56:31 +0000 The present paper is devoted to the study of the generalized projection , where is a uniformly convex and uniformly smooth Banach space and is a nonempty closed (not necessarily convex) set in . Our main result is the density of the points having unique generalized projection over nonempty close sets in . Some minimisation principles are also established. An application to variational problems with nonconvex sets is presented. Messaoud Bounkhel Copyright © 2015 Messaoud Bounkhel. All rights reserved. Existence Results for New Weak and Strong Mixed Vector Equilibrium Problems on Noncompact Domain Mon, 22 Jun 2015 11:18:01 +0000 We introduce and consider two new mixed vector equilibrium problems, that is, a new weak mixed vector equilibrium problem and a new strong mixed vector equilibrium problem which are combinations of certain vector equilibrium problems, and vector variational inequality problems. We prove existence results for the problems in noncompact setting. Ali Farajzadeh, Kasamsuk Ungchittrakool, and Apisit Jarernsuk Copyright © 2015 Ali Farajzadeh et al. All rights reserved. The Periodic Boundary Value Problem for a Quasilinear Evolution Equation in Besov Spaces Mon, 22 Jun 2015 10:05:32 +0000 This paper is concerned with the periodic boundary value problem for a quasilinear evolution equation of the following type: , , . Under some conditions, we prove that this equation is locally well-posed in Besov space . Furthermore, we study the continuity of the solution map for this equation in . Our work improves some earlier results. Yun Wu, Zhengrong Liu, and Xiang Zhang Copyright © 2015 Yun Wu et al. All rights reserved. Existence and Multiplicity of Fast Homoclinic Solutions for a Class of Nonlinear Second-Order Nonautonomous Systems in a Weighted Sobolev Space Mon, 22 Jun 2015 07:01:44 +0000 This paper is concerned with the following nonlinear second-order nonautonomous problem: , where , , and , are not periodic in and is a continuous function and with . The existence and multiplicity of fast homoclinic solutions are established by using Mountain Pass Theorem and Symmetric Mountain Pass Theorem in critical point theory. Qiongfen Zhang and Yuan Li Copyright © 2015 Qiongfen Zhang and Yuan Li. All rights reserved. Long Time Decay Rate to a Bipolar Quantum Drift-Diffusion Model Thu, 18 Jun 2015 08:14:03 +0000 This paper is devoted to studying the long time behavior of solutions to a bipolar quantum hydrodynamic in one-dimensional space for general pressure functions. The model is usually applied to simulate some quantum effects in semiconductor devices. The decay rate for time variable is obtained by the entropy functional method and semidiscrete technique. Yingjie Zhu, Bo Liang, and Xiting Peng Copyright © 2015 Yingjie Zhu et al. All rights reserved. Invertible Weighted Composition Operators on the Fock Space of Wed, 17 Jun 2015 08:08:55 +0000 We give a complete characterization of bounded invertible weighted composition operators on the Fock space of . Liankuo Zhao Copyright © 2015 Liankuo Zhao. All rights reserved. Weighted BMO Estimates for Toeplitz Operators on Weighted Lebesgue Spaces Tue, 16 Jun 2015 10:28:55 +0000 The authors establish the weighted BMO estimates for a class of Toeplitz operators related to strongly singular Calderón-Zygmund operators on weighted Lebesgue spaces. Moreover, the corresponding result for the Toeplitz operators related to classical Calderón-Zygmund operators can be deduced. Yan Lin and Mengmeng Zhang Copyright © 2015 Yan Lin and Mengmeng Zhang. All rights reserved. On the Geometry of Müntz Spaces Tue, 16 Jun 2015 08:55:42 +0000 Let satisfy , and . We investigate the Müntz spaces for . We show that, for each , there is a Müntz space which contains isomorphic copies of all Müntz spaces as complemented subspaces. is uniquely determined up to isomorphisms by this maximality property. We discuss explicit descriptions of . In particular is isomorphic to a Müntz space where consists of positive integers. Finally we show that the Banach spaces for and for are always isomorphic to suitable Müntz spaces if the are the spans of arbitrary finitely many monomials over . Sergey V. Ludkovsky and Wolfgang Lusky Copyright © 2015 Sergey V. Ludkovsky and Wolfgang Lusky. All rights reserved. Note on Order-Isomorphic Isometric Embeddings of Some Recent Function Spaces Mon, 08 Jun 2015 07:59:54 +0000 We investigate certain recently introduced ODE-determined varying exponent spaces. It turns out that these spaces are finitely representable in a concrete universal varying exponent space. Moreover, this can be accomplished in a natural unified fashion. This leads to order-isomorphic isometric embeddings of all of the above spaces to an ultrapower of the above varying exponent space. Jarno Talponen Copyright © 2015 Jarno Talponen. All rights reserved. Space of Functions with Some Generalization of Bounded Variation in the Sense of de La Vallée Poussin Thu, 04 Jun 2015 10:25:00 +0000 We introduce a function space with some generalization of bounded variation in the sense of de la Vallée Poussin and study some of its properties, like embeddings and decompositions, among others. René Erlín Castillo, Humberto Rafeiro, and Eduard Trousselot Copyright © 2015 René Erlín Castillo et al. All rights reserved. Hypercyclic Behavior of Translation Operators on Spaces of Analytic Functions on Hilbert Spaces Wed, 03 Jun 2015 11:18:26 +0000 We consider special Hilbert spaces of analytic functions of many infinite variables and examine composition operators on these spaces. In particular, we prove that under some conditions a translation operator is bounded and hypercyclic. Zoryana Mozhyrovska and Andriy V. Zagorodnyuk Copyright © 2015 Zoryana Mozhyrovska and Andriy V. Zagorodnyuk. All rights reserved. On Interval-Valued Pseudolinear Functions and Interval-Valued Pseudolinear Optimization Problems Tue, 02 Jun 2015 10:55:03 +0000 Some basic characterizations of an interval-valued pseudolinear function are derived. By means of the properties of interval-valued pseudolinearity, a class of interval-valued pseudolinear programs is considered, and the solution set of the interval-valued pseudolinear optimization problem is characterized. Jianke Zhang, Qinghua Zheng, Chang Zhou, Xiaojue Ma, and Lifeng Li Copyright © 2015 Jianke Zhang et al. All rights reserved.